This document discusses how students learn mathematics and the key principles involved. It describes three principles of how people learn: engaging prior understandings, the essential role of factual knowledge and conceptual frameworks, and the importance of self-monitoring. It also discusses the strands of mathematical proficiency and preconceptions that students have about mathematics. The document concludes by outlining instructional challenges and features that support developing students' mathematical understanding.
A report on Metacognition
Contents:
Definition of Metacognition
Elements of Metacognition
Identifying the Elements of Metacognition
Uses of Metacognition
Teaching Strategies for Metacognition
Questions to Improve Metacognition
A report on Metacognition
Contents:
Definition of Metacognition
Elements of Metacognition
Identifying the Elements of Metacognition
Uses of Metacognition
Teaching Strategies for Metacognition
Questions to Improve Metacognition
Pilot experiment courses at the University of Nebraska-Lincoln, embedding "Coaching Metacognition" and "Web Literacy" into main core subject-content curriculum as "Hidden Curricula", using Connectivist Open Online Learning (COOL) technology tools and techniques.
Presentation at the 2014 Online & Blended Colloquium by Roz Hussin, Bill Lopez, and Jane Hanson, on April 14, 2014.
This paper covers six major learning theories for Academic Advisors. It gives an overview of each theory and notes where students may struggle and strategies to help students succeed.
Pilot experiment courses at the University of Nebraska-Lincoln, embedding "Coaching Metacognition" and "Web Literacy" into main core subject-content curriculum as "Hidden Curricula", using Connectivist Open Online Learning (COOL) technology tools and techniques.
Presentation at the 2014 Online & Blended Colloquium by Roz Hussin, Bill Lopez, and Jane Hanson, on April 14, 2014.
This paper covers six major learning theories for Academic Advisors. It gives an overview of each theory and notes where students may struggle and strategies to help students succeed.
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Presentatie over de zakelijke mogelijkheden van social media, zoals verzorgd op 20 november j.l. op het ROC van Twente.
Nuttige links:
https://jochemkoole.nl
http://www.kennisnet.nl/fileadmin/contentelementen/kennisnet/sociale_media/folder-socialmedia_ROCvanTwente.pdf
http://socialmediawijs.nl/aanbod/licenties/social-media-rijbewijs-mbo-licentie/
http://feedly.com
http://mention.net
http://talkwalker.com/alerts/
XVII Международная книжная выставка-ярмарка "Зеленая волна", 1-4 августа, 2013, Одесса, ул. Дерибасовская, I Одесский Корнейчуковский фестиваль детской литературы
#KC Social Media Command Center - All-Star GameMatt Staub
Presentation from the September 7, 2012 Social Media Club of Kansas City Breakfast, featuring the community-led Social Media Command Center for the MLB All-Star Game.
Learn how Merit addresses the perception gap that prevents higher education from communicating the value of a degree to students, parents and employers.
A Beginner's Guide for Teaching MathematicsAslam Bagdadi
This deals with the nature of mathematics, methods and strategies for teaching learners including the use of technology. It is also discusses how math curriculum can be used to measure intelligence.
Note: This is a curation of other slideshows found in slideshare.
Teaching Mathematics with Innovative Methodsijcnes
In every society and in every age, a system of education is evolved according to its need and the temper of its times. Actually education means the development of habits, attitudes and skills which help a man to lead a full and worthwhile life. It is not just storage of information. Various teaching methods that can be adopted in colleges or higher educational institutions create a congenial learning environment in the teaching learning situations. The learner centered teaching methods are the co �operative endeavors to be followed both by the teacher and students. Such approaches remove passivity, dullness, non performance of the students. Without much difficulty, the teacher can shift his teaching strategy from lecturing to the learner- centered approaches. Teachers must have accurate knowledge of the subject, ability to bring the subject matter to the level of student understanding, self confidence, ability of expression, knowledge of evolution techniques, ability in questioning and respect for students opinion. The methods like Flanders interaction analysis, verbal interaction category system, reciprocal category system and equivalent talk category system may be employed for better teaching
Cognitive Load Theory, conceptualized by educational psychologist John Sweller in the late 1980s, stands as a cornerstone in the realm of instructional design. The theory fundamentally addresses how working memory processes information and how educators can strategically manage the cognitive load imposed on students during the learning process. To
Teacher Effectiveness Impacts Student Success in PreK and Kindergarten MathETA hand2mind
Core PD 'Where's the Math?' course on early childhood math professional development, by Juanita V. Copley, Ph.D., focuses on equipping teachers with the content knowledge and instructional strategies to ensure that young children encounter good mathematics instruction in their early years of schooling.
1. ITLM TOPIC 4
HOW STUDENTS LEARN AND
UNDERSTANDING OF MATHEMATICAL
STRANDS
2. OBJECTIVES
Be aware and describe the principles of how
students learn and acquire mathematical
knowledge as a basis for designing an
instruction.
Understand and describe the mathematical
strands in learning mathematics.
3. HOW PEOPLE LEARN
Principle 1: Engaging Prior Understandings
Principle 2: The Essential Role of Factual
Knowledge and Conceptual Frameworks in
Understanding
Principle 3: The Importance of Self-
Monitoring
4. PRINCIPLE 1
A fundamental insight about learning is that
new understandings are constructed on a
foundation of existing understandings and
experiences
The understandings children carry with them
into the classroom, even before the start of
formal schooling, will shape significantly how
they make sense of what they are taught
5. PRINCIPLE 2
Learning with understanding affects our
ability to apply what is learned
This concept of learning with understanding
has two parts:
factualknowledge must be placed in a
conceptual framework to be well understood;
and
concepts are given meaning by multiple
representations that are rich in factual detail.
6. PRINCIPLE 3
“You are the owners and operators of your
own brain, but it came without an instruction
book. We need to learn how we learn.”
A “metacognitive” or self-monitoring
approach can help students develop the
ability to take control of their own
learning, consciously define learning
goals, and monitor their progress in
achieving them.
8. MATHEMATICAL PROFICIENCY
Conceptual understanding — comprehension
of mathematical concepts, operations, and
relations
Procedural fluency — skill in carrying out
procedures
flexibly, accurately, efficiently, and
appropriately
Strategic competence — ability to
formulate, represent, and solve mathematical
problems
9. MATHEMATICAL PROFICIENCY
Adaptive reasoning—capacity for logical
thought, reflection, explanation, and
justification
Productive disposition—habitual inclination to
see mathematics as sensible, useful, and
worthwhile, coupled with a belief in diligence
and one’s own efficacy
10. PRECONCEPTIONS ABOUT MATHEMATICS
Preconception 1: Mathematics is about
learning to compute
Preconception 2: Mathematics is about
“following rules” to guarantee correct
answers
Preconception 3: Some people have the
ability to “do math” and some don’t
11. INSTRUCTIONAL CHALLENGES
First, how can we teach mathematics so
students come to appreciate that it is not
about computation and following rules, but
about solving important and relevant
quantitative problems?
Second, how can we link formal mathematics
training with students’ informal knowledge
and problem-solving capacities?
12. INSTRUCTIONAL CHALLENGES
There is surely no single best instructional
approach,
But it is possible to identify certain features of
instruction that support the above goals:
AllowingMultiple Strategies
Encouraging Math Talk
Designing Bridging Instructional Activities
13. ASSIGNMENT
Read the articles in Constructivism, Situated
Learning, and Other Learning Theories
Work in pair, and choose one learning theory for
each pair.
Write summary of the learning theory you have
chosen.
Choose one mathematics topic and apply the
learning theory for teaching the topic chosen.
Present the summary in front of the class.
15. LEARNING ENVIRONMENT
The learner-centered lens encourages
attention to preconceptions, and begins
instruction with what students think and
know.
The knowledge-centered lens focuses on
what is to be taught, why it is taught, and
what mastery looks like.
16. LEARNING ENVIRONMENT
The assessment-centered lens emphasizes
the need to provide frequent opportunities to
make students’ thinking and learning visible
as a guide for both the teacher and the
student in learning and instruction
The community-centered lens encourages a
culture of questioning, respect, and risk
taking.
Editor's Notes
Most of the students feel that there are so many formulas to remember in Trigonometry. It makes them frequently feel confused which one fix to use in solving a problem. In addition, they always have misconception on algebraic properties of trigonometric forms. For example, they frequently write sin 2x to be equal to 2 sin x. Moreover some of them also consider that sin2x equals to sin 2x. The most difficult one for them is the way and in what condition they can apply their knowledge.
For example, when told that the earth is round, children may look to reconcile this information with their experience with balls. It seems obvious that one would fall off a round object.
This essential link between the factual knowledge base and a conceptual framework can help illuminate a persistent debate in education: whether we need to emphasize “big ideas” more and facts less, or are producing graduates with a factual knowledge base that is unacceptably thin. While these concerns appear to be at odds, knowledge of facts and knowledge of important organizing ideas are mutually supportive. Studies of experts and novices—in chess, engineering, and many other domains—demonstrate that experts know considerably more relevant detail than novices in tasks within their domain and have better memory for these details. But the reason they remember more is that what novices see as separate pieces of information, experts see as organized sets of ideas.
“Meta” is a prefix that can mean after, along with, or beyond. In the psychological literature, “metacognition” is used to refer to people’s knowledge about themselves as information processors. This includes knowledge about what we need to do in order to learn and remember information (e.g., most adults know that they need to rehearse an unfamiliar phone number to keep it active in short-term memory while they walk across the room to dial the phone). And it includes the ability to monitor our current understanding to make sure we understand. Other examples include monitoring the degree to which we have been helpful to a group working on a project. The concept of metacognition includes an awareness of the need to ask how new knowledge relates to or challenges what one already knows—questions that stimulate additional inquiry that helps guide further learning.Supporting students to become aware of and engaged in their own learning will serve them well in all learning endeavors. To be optimally effective, however, some metacognitive strategies need to be taught in the context of individual subject areas. For example, guiding one’s learning in a particular subject area requires awareness of the disciplinary standards for knowing. To illustrate, asking the question “What is the evidence for this claim?” is relevant whether one is studying history, science, or mathematics. However, what counts as evidence often differs. In mathematics, for example, formal proof is very important. In science, formal proofs are used when possible, but empirical observations and experimental data also play a major role. In history, multiple sources of evidence are sought and attention to the perspective from which an author writes and to the purpose of the writing is particularly important. Overall, knowledge of the discipline one is studying affects people’s abilities to monitor their own understanding and evaluate others’ claims effectively.
Instruction must begin with close attention to students’ ideas, knowledge, skills, and attitudes, which provide the foundation on which new learning builds. Sometimes learners’ existing ideas lead to misconceptions. More important, however, those existing conceptions can also provide a path to new understandings. The ideas and experiences of students provide a route to new understandings both about and beyond their experience.Being learner-centered, then, involves paying attention to students’ backgrounds and cultural values, as well as to their abilities. To build effectively on what learners bring to the classroom, teachers must pay close attention to individual students’ starting points and to their progress on learning tasks. They must present students with “just-manageable difficulties”—challenging enough to maintain engagement and yet not so challenging as to lead to discouragement. They must find the strengths that will help students connect with the information being taught. Unless these connections are made explicitly, they often remain inert and so do not support subsequent learning.